Explicit construction of effective flux functions for Riemann solutions

TL;DR

This paper presents a method to explicitly construct scalar flux functions that accurately represent solutions to Riemann problems in systems of conservation laws.

Contribution

It introduces a novel explicit construction technique for effective flux functions tailored to Riemann solutions.

Findings

Constructed flux functions accurately describe Riemann solutions.

Method simplifies analysis of complex conservation law systems.

Provides a new tool for solving Riemann problems explicitly.

Abstract

For a family of Riemann problems for systems of conservation laws, we construct a flux function that is scalar and is capable of describing the Riemann solution of the original system.